Question: Solve for $x$ and $y$ using elimination. ${5x+3y = 37}$ ${6x+3y = 42}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${5x+3y = 37}$ $-6x-3y = -42$ Add the top and bottom equations together. $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x+3y = 37}\thinspace$ to find $y$ ${5}{(5)}{ + 3y = 37}$ $25+3y = 37$ $25{-25} + 3y = 37{-25}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {6x+3y = 42}\thinspace$ and get the same answer for $y$ : ${6}{(5)}{ + 3y = 42}$ ${y = 4}$